Deformations of reducible representations of 3–manifold groups into PSL2(ℂ)

Heusener, Michael; Porti, Joan

doi:10.2140/agt.2005.5.965

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Deformations of reducible representations of 3–manifold groups into $\mathrm{PSL}_2(\mathbb{C})$

Michael Heusener and Joan Porti

Algebraic & Geometric Topology 5 (2005) 965–997

DOI: 10.2140/agt.2005.5.965

arXiv: math.GT/0411365

Abstract

Let $M$ be a 3–manifold with torus boundary which is a rational homology circle. We study deformations of reducible representations of $π_{1} (M)$ into ${PSL}_{2} (ℂ)$ associated to a simple zero of the twisted Alexander polynomial. We also describe the local structure of the representation and character varieties.

Keywords

variety of representations, character variety, rational homology circle

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 20C99, 57M05

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Publication

Received: 16 November 2004

Revised: 30 May 2005

Accepted: 25 July 2005

Published: 11 August 2005

Authors

Michael Heusener
Laboratoire de Mathématiques Université Blaise Pascal 63177 Aubière Cedex France

Joan Porti
Departament de Matemàtiques Universitat Autònoma de Barcelona E-08193 Bellaterra Spain

Volume 5, issue 3 (2005)